How to assign same Data to multiple object copies
Blender makes this very easy.

Select all the objects you want to have the same data, then select the object which the data will be copied from, last so that is it the active object.

Press CtrlL and choose Object Data. Or from the 3D view header Object > Make Links > Object Data.

Doing that will give the same outcome as if you had used the linked duplicates (AltD) to start with.